(a) If antilog 1.5662 = 36.83, then find the value of the following :(

1.	(a) If antilog 1.5662 = 36.83, then find the value of the following :(i) antilog \(\bar{1}\).5662(ii) antilog 2.5662(iii) antilog \(\bar{2}\).5662(b) Find the value of antilog (log x).
Answer» (a) Given, antilog 1.5662 = 36.83 (i) ∵ Mantissa of 1.5662 and 1.5662 are same. So, anitlog of two number will be same digit numbers. Now, characteristics of which number is 1 then there will be no zero after decimal point in antilog. ∴ Required antilog \(\bar{1}\).5662 = 0.3683. (ii) ∵ Mantissas of 1.5662 and 2.5662 are same. So, antilog of two numbers will be same digit number. Now, characteristic of which number is 2 then decimal point will be after 3 digit in antilog. ∴ Required anitlog 2.5662 = 368.3. (iii) ∵ Mantìssa of 1.5662 and \(\bar{2}\).5662 are same. So. antilog of two numbers will be same digit number. Now, characteristic of which number is \(\bar{2}\) then there will be one zero after decimal point in anitlog. ∴ Required antilog \(\bar{2}\).5662 = 0.03683. (b) antilog and log are opposite to each other. ∴ antilog (log x) x.

(a) If antilog 1.5662 = 36.83, then find the value of the following :(i) antilog \(\bar{1}\).5662(ii) antilog 2.5662(iii) antilog \(\bar{2}\).5662(b) Find the value of antilog (log x).

Answer»

(a) Given, antilog 1.5662 = 36.83

(i) ∵ Mantissa of 1.5662 and 1.5662 are same.

So, anitlog of two number will be same digit numbers.

Now, characteristics of which number is 1 then there will be no zero after decimal point in antilog.

∴ Required antilog \(\bar{1}\).5662 = 0.3683.

(ii) ∵ Mantissas of 1.5662 and 2.5662 are same.

So, antilog of two numbers will be same digit number.

Now, characteristic of which number is 2 then decimal point will be after 3 digit in antilog.

∴ Required anitlog 2.5662 = 368.3.

(iii) ∵ Mantìssa of 1.5662 and \(\bar{2}\).5662 are same.

So. antilog of two numbers will be same digit number.

Now, characteristic of which number is \(\bar{2}\) then there will be one zero after decimal point in anitlog.

∴ Required antilog \(\bar{2}\).5662 = 0.03683.

(b) antilog and log are opposite to each other.

∴ antilog (log x) x.